The introduction might include reference to the wider implications of the study
e.g. for humans.
When you are drawing conclusions from statistical tests it is helpful to say
if the pattern were due to drift alone we might expect to see xxxx
if it were due to selection and drift we might expect to see xxx
if it were due to selection with little drift ...
If gene flow influence the patterns ...
etc
What we actually saw was ...
this can be interpreted in the following way
The null hypothesis is that there is no difference between the allele frequencies in the populations (not that there is no SIGNIFICANT difference).
In other words any difference between the samples was due to the unavoidable sampling variation (remember, that is different from experimental error!).
If the null is true, then it is unlikely (but not impossible) that the test will report a significant difference.
If there is a significant difference, that might be due to selection, or drift, or in some circumstances gene flow.
You have to use some other logic (in addition to a small p-value) to tell these alternatives apart.
Differences within the same habitat-type might be due to drift.
Differences among habitat types might be due to drift or selection, but selection would would be expected to produce CONSISTENT differences, whereas drift would produce variable differences.
Don't repeat in text what you have presented in a table
Just because your results are unexpected it does not mean it is impossible to form any reliable conclusions-
you need to say what can be ruled in and what can be ruled out.
It is wise to test if there is variation within the same habitat-type before testing for variation between
habitats. Otherwise you cannot rule out the possibility that there are large differences - perhaps due to drift - unrelated to our habitat classifications.
A p value DOES NOT tell you the probability that the null hypothesis is true!
It asks the question, if the null hypothesis were true, how likely would it be to get a value of the statistic this extreme or larger due to the sampling variation?
The convention is that a P-value should be smaller than 0.05 before alternatives to the null hypothesis are considered.
If you have no evidence for the action of selection from differences among locations, it seems unjustified to conclude that the high frequency of one
particular colour is due to selection. Why not drift (e.g. yellow has been luck in this region) ?
Of course it could be selection, but do you have any evidence for that ?
You cannot be sure that there is no gene flow over any given difference. You might assume it (and make it clear that it is only an assumption) or you might test it in some way.
Statistical tests other than a chi^2 test are possible, but need to be justified
If there is no significant difference between samples, this does NOT indicate the pattern was due to drift.
Genetic drift would be expected to lead to significant differences among populations just like selection.
If you found no significant patterns, one possibility is that your sample size was too small to pick up the differences that were there.
Alternatively there could be no differences in frequency among the populations.
P-values must be between 0 and 1. Something is wrong otherwise
If you get a significant P-value then it is weak to argue the sample size is too small. The statistical test takes into account the sample size.
A dominant allele can be rare, a recessive allele can be common.
The null hypothesis is NOT that drift alone affects the sample frequencies. It is that sampling variation alone affects them. Drift can produce significant differences between samples.
There are several alternative hypotheses: differences among populations is due to sampling error, to drift, to selection, to gene flow from other areas and some combination of the last 3.
Issues that arose in previous years:
1 If you provide definitions, give a citation 2 We did not investigate the source of polymorphism, but the processes affecting its spatial distribution. Similarly we certainly cannot discern the CAUSE of selection with our studies- we might obtain evidence for its presence. 3 A 20m or 40m separation between populations might be sufficient to mean that the allele frequencies were not correlated due to gene flow (or close enough to show traces of gene flow from different habitats) - but to be sure, we would have to investigate that in our study, since we do not KNOW the relevant distances a priori. You need to be careful to distinguish assumptions which may be wrong, and the evidence you have collected. 4 The terms 'Figure 1', 'Figure 2' etc are for FIGURES pictures/graphs/maps etc. Do not use this term for tables, which (should be called 'Table 1', 'Table 2' etc). 5 When you find a difference between what is reported in some of the literature and your results, have confidence in your own results. Do not be too hasty to attempt to explain it away as experimental error. 6 Chi square tests evaluate the difference in relative frequencies between two or more populations. Hence you should report which populations are being compared, and what the categories that were being compared (e.g. populations 2 vs 3, the frequency of brown, pink, yellow unbanded, & yellow banded). It would be easier to understand the results if these were reported as a contingency table (example below), or shown graphically. 7 In order to evaluate a chi square value, you need to know the degrees of freedom 8 It is not obvious that having sample areas of different size in different localities would cause problems. If you think it would, then you need to explain why 9 If you see no significant differences, there might be biological reasons (e.g. extensive gene flow`) 10 Prof Steve Jones did not ONLY study Pyrenean snails. You know he did it in Oxfordshire too (from the videos). 11 Do not neglect drift as a process producing differences between populations 12 There were no C. hortensis on the site, only young C. nemoralis with no lip-band.
1: Some of you are confused about 'pseudo-replication' and 'sampling error' -better called 'sampling variation' IMO. (N.b. 'measurement error' can mean something similar depending on context).
‘Pseudo-replication’ refers to the case where your sampling design contains observations that are not independent. For example the high frequency of yellow shells at two locations may share a common cause (perhaps there is high gene flow between them, so the yellow frequency drifts up and down in concert). As an aside, fancy statistical methods can allow you to deal with such effects in some cases, but this type of design is best avoided if possible – so is usually best to attempt a design where observations are independent.
‘Sampling variation’ is the unavoidable variability in your sample. It is not an ‘error’, in the sense of something done incorrectly. For example, the frequency of yellow will not be exactly the frequency in the wild population. You did not sample them all: many of the snails are buried or hidden in thick vegetation. You do not expect the frequency in your sample to exactly match the frequency in the wild. However, your statistical test indicates whether differences in the observed frequency at different locations might be due to sampling error.
2: Many of you said that since you took samples from over 20m apart they were independent, as snails don’t travel that far. This is an assumption, but many of you stated this as a fact. I corrected this error on many of the online-introductions – so you should have made this important distinction, which goes to the heart of the scientific method. It is an assumption, based on what others have written about dispersal distances. However, dispersal over several generations can lead to correlations between quite distant sites. The assumption may be right, but you cannot be sure, so your write-up should make it clear that your assumption could be wrong.
3: This is a similar point to 2: you need to be more cautious in presenting your experimental design. Many of you tried to control for environmental variation e.g. by keeping height the same, and only varying the habitat type (or keeping the habitat type constant and only varying the height, etc). Again, many of you made the error that this will have worked as you assumed. You may indeed have successfully controlled for key environmental variables by keeping height constant, but we don’t know for sure that this was successful – as no one knows enough about snail ecology to be sure what the key environmental variables are. You should have said you attempted to control for other environmental variables, not that you did.
4: The number dead and alive depends on many factors – the actual size of the live population, the proportion you saw, the number that die each generation, the number of generations the dead shells last, the proportion of dead shells of each age that you will find. Hence the relative number of live and dead is difficult to interpret, and certainly does not relate directly to death rate.
5: Even if your null hypothesis is false, there may be two or more alternate hypotheses. This is the case for our study, sampling error may not explain the difference between sites, but it may be due to selection, drift, gene flow, some combination etc etc. For this reason, even if the data are unlikely under the null hypothesis, a P-value does not tell us anything about the relative probability of the alternative hypotheses (or even the null, actually… the data could be unlikely under the null, but even more unlikely under the alternate hypotheses). So we avoid saying anything other than something like ‘we reject the null hypothesis at the 5% level’.
6: The reason that Cepaea are a good model system is not really due to their ease of capture; unless you mean our ability to rapidly collect a large sample-size. The direct link from phenotype to known genotype is helpful (‘they wear their genes on their shells’, Jones pers. comm..). Also limited dispersal means that genetic differences accumulate on a small spatial scale – you can study differences within a single field, rather than having to look at whole continents.
7: The null hypothesis is that there is no difference in colour frequencies between certain locations – not that we will observe no differences (or that we observe no significant difference). After all we expect to observe differences even if the frequency is actually the same, due to the sampling variation (which is NOT an error in the sense of ‘mistake’).
8: Several groups chose colour and banding categories, which meant that their expected frequencies in some cell of their matrix were less than 3. This makes the chi-squared test unreliable. They should have combined categories or split the sample up differently.
9: This is very, very important – and I emphasised it over and over again in the lectures. The Chi-square test CANNOT tell you if genetic drift or selection explains your results. You would expect a significant difference in either case (as long as your sampling strategy was well designed and you were not unlucky in your sampling).
10: Some of you seem to have a quasi-mystical belief in the value of quadrats. Quadrats, in themselves, do not make sampling more ‘scientific’. They are helpful if, for some reason, you need to take multiple samples from areas of the same shape and dimensions. That was not the case for our samples, where we simply needed to evaluate the proportion of different coloured snails in an area.
11: Absence of evidence is not evidence of absence. Hence if you see no evidence of a difference between two localities, there may be none – but you may have been unlucky, or not had a large enough sample size to see subtle differences.
12: If you do many Chi-square tests, some of them are expected to be significant even if the null is true. If you do 20, you expect 1 to appear significant at the 5% level under the null hypothesis (this is what the 5% level means).
13: Selection for camouflage is only one possible type of selection on the visible phenotype. There are many others.
14: If you merge data from several sites, you should first check there are not significant differences between them.
15. The absence of selection does not lead to drift. Drift affects all alleles in all populations, even if they are subjected to selection.
16. If you do not reject the Null hypothesis you do not reject the Alternative Hypothesis as a consequence. You have not evaluated the relative merits of Null and Alternative.
1. Remember genetic drift can lead to the loss of a beneficial allele
2. Strong selection or strong drift can produce sudden changes in allele frequency, i.e. over short distances
3. The same selective regime could lead to different outcomes in different places, for example suppose there were selection for dark snails in wooded areas, that could be achieved by a dark background in one population, and by having five thick bands in another
4. Take care in excluding samples from an analysis, because they do not fit the general trend. This may be a legitimate exclusion of outliers. However, by doing this, you could also end up honing your data to have apparently significant patterns that fit your preconceptions.
5. If you find no significant differentiation between widely spaced locations in each habitat type, yet significant differentiation between two (or more) habitat types that does suggest drift is having a relatively small effect, and that the consistent difference between habitats is due to selection. However, you should ask yourself if the sites in the same habitat are closer together than sites in different habitats. If that is the case, then they might be more similar because of gene flow between them, rather than a consistent effect of selection. You should at least raise other possible explanations for any such consistent pattern, and evaluate them. 7. Latin names are given in italics (or underlined) and the species name starts with a lower case letter: Cepaea nemoralis. 8. If you present other scientists’ results, it is best to give a) the evidence b) what the authors inferred c) the logical path that led to it. E.g. Jones found dark snails painted white behaved like light coloured snails (and visa versa) (evidence), hence the behaviour changed when the phenotype was changed although the alleles remained the same (logic), hence he concluded that alleles for dark shells do not directly affect behaviour but through their effect on the shell colour (what he inferred). 9. Remember the shells you collected were dead, so provide a summary of the genotypes that have lived and died over a period of several years (a decade?) in the locations where you collected 10.It’s means it is. Its means ‘belonging to it’ and has no apostrophe, just as his (belonging to him) has no apostrophe. 11.When you cite authors in the text, you do not put their initial in the text. Eg. you write something like ‘Nichols found a hybrid zone (Nichols 1984)’; not ‘Nichols, R found a hybrid zone(Nichols, R 1984)’. You only put the initial in references at the end. 13.Do not round expected value to whole numbers
16.If your results are statistically significant, then it is rather weak to say that they could be due to sampling error – the whole point of the significant test is to show that is unlikely.
21.Be careful with the term ‘preference’. That implies a behavioural choice, e.g. for moving towards or staying in a particular habitat. That is different to selection acting to cull the unsuitable phenotypes from a habitat – which requires no preference on behalf of the snails.
22.Gene flow does not always create or sustain polymorphism; rather it moves alleles from one habitat to another. Hence gene flow might produce polymorphism on the boundary between two habitats under divergent selection. On the other hand reduced gene flow can prevent a whole area becoming fixed for one allele by drift (or selection), hence sustaining polymorphism.
Common issues that arose last year
e.g. for humans.
if the pattern were due to drift alone we might expect to see xxxx
if it were due to selection and drift we might expect to see xxx
if it were due to selection with little drift ...
If gene flow influence the patterns ...
etc
What we actually saw was ...
this can be interpreted in the following way
In other words any difference between the samples was due to the unavoidable sampling variation (remember, that is different from experimental error!).
If the null is true, then it is unlikely (but not impossible) that the test will report a significant difference.
If there is a significant difference, that might be due to selection, or drift, or in some circumstances gene flow.
You have to use some other logic (in addition to a small p-value) to tell these alternatives apart.
Differences within the same habitat-type might be due to drift.
Differences among habitat types might be due to drift or selection, but selection would would be expected to produce
CONSISTENT differences, whereas drift would produce variable differences.
you need to say what can be ruled in and what can be ruled out.
habitats. Otherwise you cannot rule out the possibility that there are large differences - perhaps due to drift - unrelated to our habitat classifications.
It asks the question, if the null hypothesis were true, how likely would it be to get a value of the statistic this extreme or larger due to the sampling variation?
The convention is that a P-value should be smaller than 0.05 before alternatives to the null hypothesis are considered.
particular colour is due to selection. Why not drift (e.g. yellow has been luck in this region) ?
Of course it could be selection, but do you have any evidence for that ?
Genetic drift would be expected to lead to significant differences among populations just like selection.
Alternatively there could be no differences in frequency among the populations.
Issues that arose in previous years:
1 If you provide definitions, give a citation
2 We did not investigate the source of polymorphism, but the processes affecting its spatial distribution. Similarly we certainly cannot discern the CAUSE of selection with our studies- we might obtain evidence for its presence.
3 A 20m or 40m separation between populations might be sufficient to mean that the allele frequencies were not correlated due to gene flow (or close enough to show traces of gene flow from different habitats) - but to be sure, we would have to investigate that in our study, since we do not KNOW the relevant distances a priori. You need to be careful to distinguish assumptions which may be wrong, and the evidence you have collected.
4 The terms 'Figure 1', 'Figure 2' etc are for FIGURES pictures/graphs/maps etc. Do not use this term for tables, which (should be called 'Table 1', 'Table 2' etc).
5 When you find a difference between what is reported in some of the literature and your results, have confidence in your own results. Do not be too hasty to attempt to explain it away as experimental error.
6 Chi square tests evaluate the difference in relative frequencies between two or more populations. Hence you should report which populations are being compared, and what the categories that were being compared (e.g. populations 2 vs 3, the frequency of brown, pink, yellow unbanded, & yellow banded). It would be easier to understand the results if these were reported as a contingency table (example below), or shown graphically.
7 In order to evaluate a chi square value, you need to know the degrees of freedom
8 It is not obvious that having sample areas of different size in different localities would cause problems. If you think it would, then you need to explain why
9 If you see no significant differences, there might be biological reasons (e.g. extensive gene flow`)
10 Prof Steve Jones did not ONLY study Pyrenean snails. You know he did it in Oxfordshire too (from the videos).
11 Do not neglect drift as a process producing differences between populations
12 There were no C. hortensis on the site, only young C. nemoralis with no lip-band.
1: Some of you are confused about 'pseudo-replication' and 'sampling error' -better called 'sampling variation' IMO. (N.b. 'measurement error' can mean something similar depending on context).
‘Pseudo-replication’ refers to the case where your sampling design contains observations that are not independent. For example the high frequency of yellow shells at two locations may share a common cause (perhaps there is high gene flow between them, so the yellow frequency drifts up and down in concert). As an aside, fancy statistical methods can allow you to deal with such effects in some cases, but this type of design is best avoided if possible – so is usually best to attempt a design where observations are independent.
‘Sampling variation’ is the unavoidable variability in your sample. It is not an ‘error’, in the sense of something done incorrectly. For example, the frequency of yellow will not be exactly the frequency in the wild population. You did not sample them all: many of the snails are buried or hidden in thick vegetation. You do not expect the frequency in your sample to exactly match the frequency in the wild. However, your statistical test indicates whether differences in the observed frequency at different locations might be due to sampling error.
2: Many of you said that since you took samples from over 20m apart they were independent, as snails don’t travel that far. This is an assumption, but many of you stated this as a fact. I corrected this error on many of the online-introductions – so you should have made this important distinction, which goes to the heart of the scientific method. It is an assumption, based on what others have written about dispersal distances. However, dispersal over several generations can lead to correlations between quite distant sites. The assumption may be right, but you cannot be sure, so your write-up should make it clear that your assumption could be wrong.
3: This is a similar point to 2: you need to be more cautious in presenting your experimental design. Many of you tried to control for environmental variation e.g. by keeping height the same, and only varying the habitat type (or keeping the habitat type constant and only varying the height, etc). Again, many of you made the error that this will have worked as you assumed. You may indeed have successfully controlled for key environmental variables by keeping height constant, but we don’t know for sure that this was successful – as no one knows enough about snail ecology to be sure what the key environmental variables are. You should have said you attempted to control for other environmental variables, not that you did.
4: The number dead and alive depends on many factors – the actual size of the live population, the proportion you saw, the number that die each generation, the number of generations the dead shells last, the proportion of dead shells of each age that you will find. Hence the relative number of live and dead is difficult to interpret, and certainly does not relate directly to death rate.
5: Even if your null hypothesis is false, there may be two or more alternate hypotheses. This is the case for our study, sampling error may not explain the difference between sites, but it may be due to selection, drift, gene flow, some combination etc etc. For this reason, even if the data are unlikely under the null hypothesis, a P-value does not tell us anything about the relative probability of the alternative hypotheses (or even the null, actually… the data could be unlikely under the null, but even more unlikely under the alternate hypotheses). So we avoid saying anything other than something like ‘we reject the null hypothesis at the 5% level’.
6: The reason that Cepaea are a good model system is not really due to their ease of capture; unless you mean our ability to rapidly collect a large sample-size. The direct link from phenotype to known genotype is helpful (‘they wear their genes on their shells’, Jones pers. comm..). Also limited dispersal means that genetic differences accumulate on a small spatial scale – you can study differences within a single field, rather than having to look at whole continents.
7: The null hypothesis is that there is no difference in colour frequencies between certain locations – not that we will observe no differences (or that we observe no significant difference). After all we expect to observe differences even if the frequency is actually the same, due to the sampling variation (which is NOT an error in the sense of ‘mistake’).
8: Several groups chose colour and banding categories, which meant that their expected frequencies in some cell of their matrix were less than 3. This makes the chi-squared test unreliable. They should have combined categories or split the sample up differently.
9: This is very, very important – and I emphasised it over and over again in the lectures. The Chi-square test CANNOT tell you if genetic drift or selection explains your results. You would expect a significant difference in either case (as long as your sampling strategy was well designed and you were not unlucky in your sampling).
10: Some of you seem to have a quasi-mystical belief in the value of quadrats. Quadrats, in themselves, do not make sampling more ‘scientific’. They are helpful if, for some reason, you need to take multiple samples from areas of the same shape and dimensions. That was not the case for our samples, where we simply needed to evaluate the proportion of different coloured snails in an area.
11: Absence of evidence is not evidence of absence. Hence if you see no evidence of a difference between two localities, there may be none – but you may have been unlucky, or not had a large enough sample size to see subtle differences.
12: If you do many Chi-square tests, some of them are expected to be significant even if the null is true. If you do 20, you expect 1 to appear significant at the 5% level under the null hypothesis (this is what the 5% level means).
13: Selection for camouflage is only one possible type of selection on the visible phenotype. There are many others.
14: If you merge data from several sites, you should first check there are not significant differences between them.
15. The absence of selection does not lead to drift. Drift affects all alleles in all populations, even if they are subjected to selection.
16. If you do not reject the Null hypothesis you do not reject the Alternative Hypothesis as a consequence. You have not evaluated the relative merits of Null and Alternative.
1. Remember genetic drift can lead to the loss of a beneficial allele
2. Strong selection or strong drift can produce sudden changes in allele frequency, i.e. over short distances
3. The same selective regime could lead to different outcomes in different places, for example suppose there were selection for dark snails in wooded areas, that could be achieved by a dark background in one population, and by having five thick bands in another
4. Take care in excluding samples from an analysis, because they do not fit the general trend. This may be a legitimate exclusion of outliers. However, by doing this, you could also end up honing your data to have apparently significant patterns that fit your preconceptions.
5. If you find no significant differentiation between widely spaced locations in each habitat type, yet significant differentiation between two (or more) habitat types that does suggest drift is having a relatively small effect, and that the consistent difference between habitats is due to selection. However, you should ask yourself if the sites in the same habitat are closer together than sites in different habitats. If that is the case, then they might be more similar because of gene flow between them, rather than a consistent effect of selection. You should at least raise other possible explanations for any such consistent pattern, and evaluate them.
7. Latin names are given in italics (or underlined) and the species name starts with a lower case letter: Cepaea nemoralis.
8. If you present other scientists’ results, it is best to give a) the evidence b) what the authors inferred c) the logical path that led to it. E.g. Jones found dark snails painted white behaved like light coloured snails (and visa versa) (evidence), hence the behaviour changed when the phenotype was changed although the alleles remained the same (logic), hence he concluded that alleles for dark shells do not directly affect behaviour but through their effect on the shell colour (what he inferred).
9. Remember the shells you collected were dead, so provide a summary of the genotypes that have lived and died over a period of several years (a decade?) in the locations where you collected
10.It’s means it is. Its means ‘belonging to it’ and has no apostrophe, just as his (belonging to him) has no apostrophe.
11.When you cite authors in the text, you do not put their initial in the text. Eg. you write something like ‘Nichols found a hybrid zone (Nichols 1984)’; not ‘Nichols, R found a hybrid zone(Nichols, R 1984)’. You only put the initial in references at the end.
13.Do not round expected value to whole numbers
16.If your results are statistically significant, then it is rather weak to say that they could be due to sampling error – the whole point of the significant test is to show that is unlikely.
21.Be careful with the term ‘preference’. That implies a behavioural choice, e.g. for moving towards or staying in a particular habitat. That is different to selection acting to cull the unsuitable phenotypes from a habitat – which requires no preference on behalf of the snails.
22.Gene flow does not always create or sustain polymorphism; rather it moves alleles from one habitat to another. Hence gene flow might produce polymorphism on the boundary between two habitats under divergent selection. On the other hand reduced gene flow can prevent a whole area becoming fixed for one allele by drift (or selection), hence sustaining polymorphism.